We prove that the Birkhoff normal form of hamiltonian flows at a nonresonant singular point with given quadratic part is always convergent or generically divergent. The same result is proved for the normalization mapping and any formal first integral. Introduction In this article we study analytic (R or C-analytic) hamiltonian flows xk ˙ yk ˙ ∂H , ∂yk ∂H = − , ∂xk = + where xk , yk ∈ C (resp. R), k = 1, 2, . . . n, and H is an analytic hamiltonian with power series expansion at 0 beginning with quadratic terms (so that 0.
